The arbitrary monic polynomial with distinct real roots r1, r2 is of the form: p(r) =...

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The arbitrary monic polynomial with distinct real roots r1, r2 is of the form: p(r) = r² (r₁+r₂)r +r₁r₂ find the solutions to the IVPS: - With the ODE y" — (r₁ +r₂)y' + r₁r2y = 0, Φι(0) = 1, 2 (0) = 0, φ1 (0) = 0 2 (0) = 1 (b) The arbitrary monic polynomial with complex roots o iw is of the form: p(r) = r² - 2or + (o² +w²) With the ODE y" - 2oy' + (o²+w²) y = 0, find the solutions to the IVPS: 1 (0) = 1, ₁ (0) 0 2 (0) = 0, 2(0) = 1 (c) The arbitrary monic polynomial with a repeated real root ro is of the form: p(r) = r²- 2ror+r² With the ODE y" - 2roy' + r²y = 0, find the solutions to the IVPS: Φι(0) = 1, Φ1 (0) = 0 2 (0) = 0, 2(0) = 1 The arbitrary monic polynomial with distinct real roots r1, r2 is of the form: p(r) = r² (r₁+r₂)r +r₁r₂ find the solutions to the IVPS: - With the ODE y" — (r₁ +r₂)y' + r₁r2y = 0, Φι(0) = 1, 2 (0) = 0, φ1 (0) = 0 2 (0) = 1 (b) The arbitrary monic polynomial with complex roots o iw is of the form: p(r) = r² - 2or + (o² +w²) With the ODE y" - 2oy' + (o²+w²) y = 0, find the solutions to the IVPS: 1 (0) = 1, ₁ (0) 0 2 (0) = 0, 2(0) = 1 (c) The arbitrary monic polynomial with a repeated real root ro is of the form: p(r) = r²- 2ror+r² With the ODE y" - 2roy' + r²y = 0, find the solutions to the IVPS: Φι(0) = 1, Φ1 (0) = 0 2 (0) = 0, 2(0) = 1